Frank den Hollander
Leiden University and EURANDOM
The Netherlands

Percolation


Abstract

The goal of percolation theory is to study the geometric
properties of random networks. In this talk I will describe
two variants of percolation:

1. a static variant, called "ordinary percolation";
2. a dynamic variant, called "invasion percolation".

My main target is to show that these two variants exhibit
remarkable similarities and remarkable differences.

Ordinary percolation is used to model the connectivity
in a random network ("What is connected to what?").
Invasion percolation is used to model the spread of
a virus through a random network ("What gets infected?").

I will present main results, open questions and key
challenges. No prior knowledge of percolation is
necessary for the talk.